# Full text of "Treatise On Analysis Vol-Ii"

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```450       INDEX

Kac's theorem: 13.11, prob. 14
Kakutani's skyscraper: 13.9, prob. 14
Kernel: 15.4, prob. 14
Khintchine's inequality: 13.21, prob. 10
Khintchine's statistical recurrence theorem:

13.11, prob. 10
Kolmogoroff-Sinai theorem: 13.12, prob.

10

Krein-Milman theorem: 12.15, prob. 5
Krylov-Weinstein theorem: 15.12, prob. 8

Lagrange's interpolation polynomial: 12.16,

prob.15
Lagrange's theorem on sums of squares:

14.2, prob. 2

Lebesgue function: 13.16, prob. 2
Lebesgue-Fubini theorem: 13.21
Lebesgue measure: 13.1
Lebesgue-Nikodym theorem: 13.15
Lebesgue's convergence theorems: 13.8
Lebesgue's decomposition theorem: 13.18
Left-invariant function on a group: 12.9
Locally closed: 12.2
Locally compact: 12.2
Locally convex topological vector space:

12.14

Locally finite family of subsets: 12.6
Locally integrable function: 13.13 and 13.16
Logmodular algebra: 15.3, prob. 9
Lower envelope of a family of real-valued

functions: 12.7
Lower integral: 13.5
Lower semicontinuous function: 12.7
Lower semicontinuous regularization of a
function: 12.7, prob. 8

M

Mahler's criterion: 14.4, prob. 9

Majorized function: 12.7

Majorized hermitian operator: 15.13, prob.

14

Marcinkiewicz's theorem: 13.21, prob. 21
Markoff-Kakutani theorem: 13.4, prob. 8
Martingale (elementary): 13.9, prob. 25
Maximal ergodic theorem: 13.9, prob. 12

Maximal ideal: 15.3

Maximal in measure: 13.12

Meager set: 12.16

Measurable mapping, set: 13.9 and 13.16

Measure: 13.1

Measure concentrated on a subset: 13.18

Measure defined by point masses: 13.1

Measure of a set: 13.7

Measure with base /A: 13.13

Mertens-Alexiewicz theorem: 12.16, prob.

12

Metrizable group: 12.9
Metrizable space, topology: 12.1
Minkowski area: 14.3, prob. 10
Minkowski's inequality: 13.11, prob. 12
Minkowski's theorem: 14.2, prob. 2
Minimum in measure: 13.12
Minorized function: 12.7
Minorized hermitian operator: 15.13, prob.

14

Mixing mapping: 15.11, prob. 15
Modulus function: 14.3
Modulus of an automorphism: 14.3
Moments of a measure: 15.13, prob. 1
Miintz's theorem: 13.11, prob. 6

N

Negligible function, subset: 13.6 and 13.16

Neumark's theorem: 15.11, prob. 11

Neutral component of a topological group:
12.8

Nondegenerate representation: 15.5

Normable algebra: 15.1

Normal element of an algebra with invo-
lution: 15.4

Normal unbounded operator: 15.12

Normalized Haar measure: 14.3

Normalizer of a subset: 12.8

Normed algebra: 15.1

Nowhere dense set: 12.16

Nuclear operator: 15.7, prob. 6

One-parameter subgroup: 14.11, prob. 12
Open set: 12.1
Opposite group: 12.8

Orbit of a point under the action of a group:
12.10 set: 13.11, prob. 11
```